The invention relates to a electronic device for generating a power signal Pav, which is a measure of the average power taken from a voltage source VB supplying a sine-shaped voltage Vs.
Such a electronic device is well-known and frequently comprises a multiplier. The operation of such a multiplier is based on a multiplication algorithm. Known multiplication algorithms are, inter alia, the xe2x80x9ctriangle-averaging multiplying techniquexe2x80x9d, the xe2x80x9ctime division multiplying techniquexe2x80x9d, the xe2x80x9cquarter-squares multiplying techniquexe2x80x9d, the xe2x80x9cvariable transconductance multiplying techniquexe2x80x9d and an algorithm composed of, in succession, xe2x80x9csamplingxe2x80x9d, xe2x80x9cA/D-conversionxe2x80x9d and xe2x80x9cdigital multiplicationxe2x80x9d. These algorithms are described in, for example, xe2x80x9cGreame J. G. and Tobey G. E., Operational Amplifier-Design and Application, McGraw-Hill, 1971, pp. 273-276xe2x80x9d and xe2x80x9cRogers A. E., Analog Computation in Engineering Design, McGraw-Hill, 1960, pp. 22-28xe2x80x9d.
The application of any one of these well-known multiplication algorithms in a electronic device for generating a power signal has the following drawbacks: limited accuracy, temperature sensitivity, complexity of the electronics and hence a high cost price. With respect to the latter algorithm it applies, more particularly, that it is very inaccurate at a low xe2x80x9csampling ratexe2x80x9d, particularly in the case of a phase shift between the voltage and the current or if the shape of the current deviates substantially from a sine shape.
It is an object of the invention to provide a electronic device which is comparatively inexpensive to manufacture by virtue of its comparatively simple structure, and which enables a power signal to be generated which is a comparatively accurate measure of the power supplied by the voltage source VB.
To achieve this, a electronic device as mentioned in the opening paragraph comprises
a circuit part I for generating a signal U which is a measure of the effective value of the voltage Vs,
a circuit part II for generating a square-wave voltage Vb which is in phase with the sine-shaped voltage Vs,
a circuit part III for generating a signal which is a measure of the product Q of a current Is supplied by the voltage source VB and the square-wave voltage Vb,
a circuit part IV for generating a signal Qav which is a measure of the average value of the signal Q, and
a circuit part V for generating a signal which is a measure of the product of the signal Qav and the signal U, the signal generated by the circuit part V forming the power signal Pav.
It has been found that a electronic device in accordance with the invention can be embodied so as to be comparatively simple. It has also been found that a electronic device in accordance with the invention enables a power signal to be generated, which is a very accurate measure of the power supplied by the voltage source VB, said power signal additionally being highly temperature-independent.
If the current Is supplied by the voltage source VB is sine-shaped and in phase with the voltage Vs, and if the square-wave voltage VB is equal to zero only at instants at which also the sine-shaped voltage Vs is equal to zero, then the power signal Pav is directly proportional to the power supplied by the voltage source. However, frequently the current Is taken from the voltage source Vb is not sine-shaped but can be described, using Fourier analysis, as the sum of an infinite number of sine-shaped terms, the first term having a frequency equal to the frequency of the sine-shaped voltage Vs, and the other terms having a frequency that is a multiple of the frequency of the sine-shaped voltage Vs. Correspondingly, the square-wave voltage Vb can be described, using said Fourier analysis, as the sum of an infinite number of sine-shaped terms. Due to the symmetry of the square-wave voltage, however, this sum only comprises terms whose frequency is an odd number of times the frequency of the sine-shaped voltage Vs. From this it can be derived that the product P of the current Is and the square-wave voltage Vb can be expressed as the sum of an infinite number of terms, each term being a product of two sine functions. Only if both sine functions in such a product have the same frequency, the relevant term of the product P has a finite average value. It can thus be mathematically derived that, in the case of such a non-sine shaped current Is and a square-wave voltage Vb which is equal to zero only if the sine-shaped voltage Vs is also equal to zero, the power signal Pav can be expressed as the sum of an infinite number of terms, each term of the square-wave voltage Vb yielding a term of the power signal Pav. The first term of the power signal Pav represents the power supplied by the voltage source VB. Dependent upon the shape of the current supplied by the voltage source VB, the second term and the higher terms of Pav will make a comparatively large, or less large, contribution to the value of Pav. In other words, the value of Pav deviates more from the first term of Pav, which represents the power supplied by the voltage source VB, as the shape of the current Is deviates more from a sine shape. It has been found, however, that in many applications the power signal Pav generated in the manner described hereinabove is a sufficiently accurate measure of the power supplied. If, however, the second term and the higher terms of the power signal Pav lead to an insufficiently accurate representation of the power supplied, then the second and, if desirable, also a random number of the higher terms of Pav can be zeroed. This is brought about by changing the shape of the square-wave voltage Vb in such a manner that it is equal to zero not only at the instants at which the voltage Vs is equal to zero but also at other instants. To achieve this, the square-wave voltage Vb becomes equal to zero N+1 times during each half period, where N is an even number, and the phase angles xcex1m corresponding to the instants at which the square-wave voltage Vb is zero are represented by the formulas
                    α        m            =                        π          -                                    α                              N                -                m                +                1                                      ⁢                          xe2x80x83                        ⁢            and            ⁢                          xe2x80x83                        ⁢                                          (                                                      4                    /                    n                                    ·                  π                                )                            ·                              (                                  1                  +                                                            ∑                                              m                        =                        1                                                                    N                        /                        2                                                              ⁢                                                                                            (                                                      -                            1                                                    )                                                m                                            ⁢                      cos                      ⁢                                              xe2x80x83                                            ⁢                                              n                        ·                                                  α                          m                                                                                                                    )                                                    =        0              ,    ⁣
wherein m is a natural number and n is an odd number larger than or equal to 3. The expression to the left of the = sign in the second formula is the amplitude of a term of the square-wave voltage Vb. As indicated hereinabove, this square-wave voltage only comprises terms whose frequency is an odd number of times the frequency of the voltage Vs. For this reason, for n=3, the expression to the left of the = sign in the second formula is equal to the amplitude of the second term of the square-wave voltage Vb. For n=5, this expression is equal to the amplitude of the third term, etc. If n=3 in said formulas, then the phase angles become xcex11=20xc2x0 and xcex12=160xc2x0. In other words, if the shape of the square-wave voltage Vb is chosen to be such that, in each half period, said square-wave voltage becomes equal to zero not only for the phase angles 0xc2x0 and 180xc2x0 but also for the phase angles 20xc2x0 and 160xc2x0, it is achieved that the second term in the sum of terms, which describes the square-wave voltage Vb, is equal to zero. As a result, the second term of the power signal Pav is also equal to zero. As a result, the difference between the first term of Pav, which represents the power supplied by the voltage source VB, and the (total) value of the power signal Pav is smaller than it would be if the square-wave voltage Vb is equal to zero only at the instants at which Vs is equal to zero. Correspondingly, the number of zero-axis crossings of the square-wave voltage Vb can be further increased by introducing zero-axis crossings for the phase angles that are obtained when n=5 in the above-mentioned formulas. In the sum of terms describing the square-wave voltage Vb, the second and the third term are equal to zero now. As a result, the second and the third term of the power signal Pav are also equal to zero. Consequently, the difference between the first term of Pav, which represents the power supplied by the voltage source VB, and the value of the power signal Pav has decreased further. In other words, the difference between the first term of the power signal Pav, which represents the actual power supplied by the voltage source VB, and the (total) value of the power signal Pav can be reduced to any value by increasing the number of zero-axis crossings of the square-wave voltage Vb. In practice it has been found that elimination of the second term or, at the most, the second and the third term from the sum describing the square-wave voltage Vb leads, in the majority of the practical applications, to a sufficiently small difference between the first term of the power signal Pav and the total value of the power signal Pav.
Satisfactory results were obtained with embodiments of a electronic device in accordance with the invention, wherein the circuit part I comprises a rectifier and a low-pass filter, and with embodiments wherein the circuit part IV comprises a low-pass filter.
In a particularly simple and hence inexpensive embodiment of a electronic device in accordance with the invention, the circuit part II and the circuit part III comprise
a switching element, and
a control circuit coupled to a control electrode of the switching element for rendering the switching element conducting and non-conducting if the phase angle xcex1m has a value at which the square-wave voltage Vb is zero.
Such a control circuit can be obtained, for example, by means of a microprocessor wherein the values of the phase angle xcex1m at which the switching element must be rendered conducting or non-conducting are fixed in a memory forming part of the microprocessor.
A electronic device in accordance with the invention can very suitably form part of a power supply circuit provided with a circuit part VI for generating a current from the sine-shaped voltage Vs, which current can be used to energize a load. This load may be, for example, a lamp.
These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter.